We propose a new way to reconstruct the ionized-bubble size distribution during the Epoch of Reionization (EoR) through the real-space cross-correlation of 21-cm and star-forming line-intensity maps. Understanding the evolution and timing of the EoR is crucial for both astrophysics and cosmology, and a wealth of information on the first sources can be extracted from the study of ionized bubbles. Nevertheless, directly mapping bubbles is challenging due to the high redshifts involved, possible selection biases, and foregrounds in 21-cm maps. Here, we exploit the real-space cross-correlation $ξ_{21,ν}$ between 21-cm and line-intensity mapping (LIM) signals to reconstruct the evolution of bubble sizes during reionization. For the first time, we show that $ξ_{21,ν}(r)$ departs from a saturation level for each separation $r$ when bubbles of size $r$ begin to form, providing a handle for the onset of bubbles of each radius. Moreover, we demonstrate that $ξ_{21,ν}$ evolves from positive to negative as the EoR progresses, reaching a minimum (i.e. maximum anti-correlation) when bubbles of radius $r$ reach peak abundance. We show that these results are robust to changes in the astrophysical model as well as the timing/topology of reionization. This real-space observable complements usual Fourier-space estimators by capturing the localized nature of bubbles, offering new insights into the sources driving cosmic reionization.

We present an analysis of the spectral energy distribution (SED) of the off-nuclear tidal disruption event (TDE) AT2024tvd during its late-time plateau phase, combining X-ray spectra and UV/optical photometry. Using a fully relativistic, compact accretion disk model with self-consistent inner-disk Comptonization, we reproduce the observed SED without significant residuals. The inferred black hole mass ${\rm log}{10}(M{\bullet}/M_\odot) \approx 6.0 \pm 0.2$, and the inferred disk parameters place AT2024tvd within known TDE-disk scaling relations ($L_{\rm bol}^{\rm disk}/L_{\rm Edd} \propto T_{\rm p}^4 \propto M_{\bullet}^{-1}$, $L_{\rm plat} \propto M_{\bullet}^{2/3}$, $R_{\rm out}/r_{\rm g} \propto M_{\bullet}^{-2/3}$). Our results show that: (i) there is no \textit{detected} star cluster or dwarf galaxy associated with the source, down to a mass limit of $\log_{10}(M_{\rm gal}/M_{\odot}) \leq 7.6$; (ii) the black hole is a wandering supermassive, rather than intermediate-mass, black hole; and (iii) the source represents an extreme case of black hole-to-host mass ratio, with $M_{\bullet}/M_{\rm gal} > 3\%$, consistent with a heavily tidally stripped nucleus. The latter aligns with cosmological simulations predicting that surviving host remnants of most wandering black holes should not retain a detectable stellar overdensity when located at small halo-centric distances. We discuss differences with previous analyses of this source and highlight why our modeling approach provides a more physically consistent solution with more reliable parameter inference.

Certification is important to guarantee the correct functioning of quantum devices. A key certification task is verifying that a device has produced a desired output state. In this work, we study this task in the context of photonic platforms, where single photons are propagated through linear optical interferometers to create large, entangled resource states for metrology, communication, quantum advantage demonstrations and for so-called linear optical quantum computing (LOQC). This setting derives its computational power from the indistinguishability of the photons, i.e., their relative overlap. Therefore, standard fidelity witnesses developed for distinguishable particles (including qubits) do not apply directly, because they merely certify the closeness to some fixed target state. We introduce a measure of fidelity suitable for this setting and show several different ways to witness it, based on earlier proposals for measuring genuine multi-photon indistinguishability. We argue that a witness based upon the discrete Fourier transform is an optimal choice. We experimentally implement this witness and certify the fidelity of several multi-photon states.

We show that a single spatially superposed 'source' mass acting on a 'probe' matter wavepacket can reveal the quantum nature of the gravitational field. For this we use a specific state preparation and measurement of the superposed source mass, including a postselection, which altogether results in a repulsive gravitational force on the probe particle. A classical gravitational field can never lead to repulsion, as the effect requires quantum interference of two distinct states of gravity. We also present a calculation in the Heisenberg picture under the formalism of weak values that illustrates how repulsion is achieved. Finally, we estimate the range of parameters (masses and the spatio-temporal extent of interference) for which the experiment is feasible.

This work establishes a systematic framework for operator construction in the non-relativistic effective field theory, incorporating both the three dimensional Euclidean symmetry and the internal symmetries. By employing double cover of the rotation group, we extend the Hilbert series to the non-relativistic systems, and eliminates redundancies introduced by the spin operator. We also generalize the Young tensor method to the non-relativistic cases through the $SU(2)$ semi-standard Young tableaux, which allows for the construction of operator bases with repeated fields at any given mass dimension. Utilizing the Young tensor technique and Hibert series as cross-check, we obtain the complete operator bases for the following cases: heavy particle (and also heavy quark) effective theory operators up to mass dimension 9; pion-less effective theory operators, including nucleon-nucleon contact interactions up to $\mathcal{O}(Q^4)$ and three-nucleon interactions at $\mathcal{O}(Q^2)$; and finally the spin-1/2 dark matter-nucleon operators up to $\mathcal{O}(v^4)$.

Bragg coherent diffraction imaging (BCDI) phase retrieval becomes rapidly difficult in the strong-phase regime, where a crystal contains distortions beyond half a lattice spacing. An important special case is the phase domain problem, where blocks of a crystal are displaced with sharp jumps at domain walls. The strong-phase, here defined as beyond $\pm π/2$, generates split Bragg peaks and dense fringe structure for which classical iterative solvers often stagnate or return different solutions from different initialisations. Here, we introduce an unsupervised Fourier Vision Transformer (Fourier ViT) to solve this block-phase, multi-domain phase-retrieval problem directly from measured 2D Bragg diffraction intensities. Fourier ViT couples reciprocal-space information globally through multiscale Fourier token mixing, while shallow convolutional front and back-ends provide local filtering and reconstruction. We validate the approach on large-scale synthetic datasets of Voronoi multi-domain crystals with strong-phase contrast under realistic noise corruptions, and on experimental diffraction from a $\mathrm{La}_{2-x}\mathrm{Ca}_x\mathrm{MnO}_4$ nanocrystal. Across the regimes considered, Fourier ViT achieves the lowest reciprocal-space mismatch ($χ^2$) among the compared methods and preserves domain-resolved phase reconstructions for increasing numbers of domains. On experimental data, with the same real-space support, Fourier ViT matches the iterative benchmark $χ^2$ while improving robustness to random initialisations, yielding a higher success rate of low-$χ^2$ reconstructions than the complex convolutional neural network baseline.

Standard harmonic-to-anharmonic thermodynamic integration (TI) is known to develop a near singularity in the integrand for solids exhibiting diffusive degrees of freedom, such as rotating functional groups or migrating defects. This pathology results in numerical challenges for estimating absolute free energies within a single thermodynamic cycle. In this work, we introduce a simple regularization that removes this singularity and yields a well-behaved integrand that can be accurately evaluated on a uniform grid. The approach -- termed Regularized End-point Gradient (REG) TI -- is demonstrated on a model system and on predicting the relative stability of paracetamol polymorphs for which quasi-free methyl rotations lead to a near singularity in standard TI. We expect REG TI to simplify anharmonic free energy calculations for solids and to potentially enable their automation.

Primordial non-Gaussianity generated by additional fields during inflation offers a compelling observational target. Heavy fields imprint characteristic oscillatory signals in non-Gaussian correlation functions of the inflaton, a process sometimes referred to as cosmological-collider physics. These distinct signatures are compelling windows into ultra-high-energy physics, but are often suppressed, making standard equilateral non-Gaussianity the most promising discovery channel in many scenarios. In this paper, we show that direct couplings between the inflaton and additional fields can lead to a wide variety of novel, observationally relevant signals which open new parameter regimes that simultaneously exhibit the characteristics of light and heavy fields. We identify these primordial signatures in the late-time observables of the large-scale structure of the Universe, where they most significantly modify the scale-dependent bias of the galaxy power spectrum to include an oscillatory modulation around a non-trivial power law. We explore the full range of parameters that phenomenologically arise in these models and study the sensitivity of current and future galaxy surveys, finding that this new class of primordial non-Gaussianity is particularly accessible in near-term surveys due to its oscillatory feature. Finally, we perform an analysis of existing data from the final release of the Baryon Oscillation Spectroscopic Survey (BOSS DR12). While we find no evidence for a signal, we demonstrate significant improvements in sensitivity over respective non-oscillatory scenarios and place the first constraints on this extended parameter space of oscillatory non-Gaussianity.

In this work, we introduce constructions for non-Abelian qLDPC codes obtained by gauging transversal Clifford gates using measurement and feedback. In particular, we identify two qualitatively different approaches to gauging qLDPC codes to obtain their non-Abelian counterparts. The first approach applies to codes that exhibit a generalized form of Poincaré duality and leads to a qLDPC non-Abelian Clifford stabilizer code, whose stabilizers are reminiscent of the action of a Type-III twisted quantum double. Our second approach applies to general qLDPC codes, and uses a graph of ancilla qubits which may be tailored to properties of the input codes to gauge a single transversal gate. For both constructions, the resulting gauged codes are shown to have properties analogous to 2D non-Abelian topological order -- e.g. the analog of a single anyon on a torus. We conclude by demonstrating that our gauging procedures enable magic state preparation via the measurement of logical Clifford gates. Consequently, our gauging constructions offer a protocol for performing non-Clifford operations on any qLDPC code.

The four-boson universality suggests the existence of the second excited tetramer state in a system of cold ${}^4\mathrm{He}$ atoms. It is not bound but could be seen as a resonance in the atom-trimer scattering. This process is rigorously calculated using the momentum-space transition operator framework with two realistic interatomic potentials. The $S$-wave phase shift and cross section show a resonant behavior below the excited trimer threshold, but there are sizable nonresonant contributions from $P$ and $D$ waves as well. The position and width of the resonant state is determined, and for the latter significant finite-range effects are found.

We study the edge state properties of a two-dimensional kagome lattice using a tight-binding approach, focusing on the role of lattice termination, spin-orbit coupling, and magnetic order. In the pristine limit, we show that the existence of localized edge states is highly sensitive to boundary geometry, with certain terminations completely suppressing edge modes. Kane-Mele spin-orbit coupling opens a bulk gap and stabilizes topologically protected helical edge states, yielding a robust $\mathbb{Z}_2$ insulating phase that is insensitive to termination details. In contrast, the combined effect of a Zeeman field and Rashba spin-orbit coupling drives the system into Chern insulating phases, with Chern numbers consistent with the number of chiral edge modes. We further demonstrate that non-coplanar magnetic textures generate multiple Chern phases through finite scalar spin chirality, with Kane-Mele coupling strongly tuning the topological gaps. Our results provide important insights into the tunability of edge states in the kagome lattice, which can be key to designing materials with novel electronic properties and topological phases.

We study the energy-momentum tensor of the spherically symmetric non-topological solitons of the $O(3)$ non-linear sigma-model with a standard kinetic term and with a symmetry breaking potential in 3+1 dimensional flat space-time. We evaluate the distributions of the corresponding energy density, shear forces and pressure and study the stability criteria for these solutions. We argue that the presence of domains with negative energy density and violation of the energy conditions most likely do not lead to destabilization of solitons.

Holographic entanglement entropy is a key concept linking quantum information theory and gravity. Since the original conjecture of Ryu and Takayanagi, holographic entanglement entropy has been generalized beyond Einstein--Hilbert gravity to include higher-curvature corrections. In most existing generalizations, however, it is implicitly assumed that the bulk spacetime geometry is Riemannian, i.e. torsion-free. Here we propose a prescription for incorporating torsion into holographic entanglement entropy in the boundary theory dual to five-dimensional Chern--Simons gravity. We argue that the entanglement entropy acquires an additional universal divergent term proportional to the logarithm of the UV cutoff, and that this term is generated solely by torsion.

The Event Horizon Telescope (EHT) is providing unprecedented high-resolution images of supermassive black holes. These images are fundamentally related to properties of the luminous accretion disks, since black holes themselves produce no light. We develop a simple prescription to relate observational features of black hole images to a toy model for the intensity profile of the associated accretion disk. We apply our model to the original EHT image of M87*, as well as to the reanalyzed image from the PRIMO algorithm, providing generic, simultaneous constraints on the mass of the black hole and properties of the accretion disk emission. While current images lack the resolution to confidently detect the photon ring, the consideration of multiple image parameters are found to contain enough information to provide constraints on the inner edge of the accretion disk along with the black hole mass. Using observed features of the original EHT image, we constrain the mass of M87* to be $6.6^{+1.2}_{-1.0}\times 10^9 M_\odot$ to 68$\%$ confidence, and find that emission may extend all the way to the black hole horizon. When instead using constraints from the PRIMO algorithm's image along with constraints on the brightness asymmetry provided by the original EHT analysis, we find M87*'s mass to be $ 6.4^{+0.7}_{-0.7}\times 10^9 M_\odot$ to 68$\%$ confidence, with the inner edge of the accretion disk between $3M$ and $5.3M$. Both analyses rule out an inner edge of the accretion disk coinciding with the innermost stable circular orbit for a Schwarzschild black hole. Furthermore, the narrow ring width reported in the PRIMO image also confidently rules out emission increasing all the way down to the black hole horizon. Further assumptions on the mass of M87* and connections between the accretion disk cutoff and physical radii allow for rudimentary black hole spin estimates.

The charged moments of a reduced density matrix provide a natural starting point for deriving symmetry-resolved Rényi and entanglement entropies, which quantify how entanglement is distributed among symmetry sectors in the presence of a global internal symmetry in a quantum many-body system. In this work, we study charged moments within the framework of Ballistic Fluctuation Theory (BFT). This theory describes large-scale ballistic fluctuations of conserved charges and associated currents and, by exploiting the height-field formulation of twist fields, gives access to the asymptotic behaviour of their two-point correlation functions. In Del Vecchio Del Vecchio et al. $[1]$, this approach was applied to the special case of branch-point twist fields used to compute entanglement entropies within the replica approach. Here, we extend those results by applying BFT to composite branch-point twist fields, obtained by inserting an additional gauge field. Focusing on free fermions, we derive analytic expressions for charged Rényi entropies both at equilibrium, in generalized Gibbs ensembles, and out of equilibrium following a quantum quench from $U(1)$ preserving pair producing integrable initial states. In the latter case, our results agree with the conjecture arising from the quasiparticle picture.

Gamma-hadron discrimination based on shower observables is essential for identifying gamma-ray astrophysical sources at the highest energies. In this work, we introduce $P^{α, T}_{\rm tail}$, a new discrimination variable for ultra-high-energy photon searches within the framework of a water-Cherenkov detector (WCD) array. The observable extends signal-integrated methods by incorporating the time structure of WCD traces, using cumulative signal distributions. Using simulated proton- and gamma-induced air showers at energies around $10^{17}\,\mathrm{eV}$, we evaluate the performance of $P^{α, T}_{\rm tail}$ and compare it with established WCD-based observables such as $S_b$, risetime-based variables, and the SWGO-inspired, $P^α_{\rm tail}$. The new variable attains a background contamination of roughly $2 \times 10^{-2}$ at $50\%$ gamma efficiency, improving upon existing WCD-only methods by nearly a factor of five and approaching the performance of an idealized muon-isolating reference. These results demonstrate the effectiveness of exploiting time-resolved signal tails to enhance ultra-high-energy photon searches in sparse surface arrays.

The amplification of magnetic fields in black hole accretion flows governs key high-energy phenomena such as magnetically arrested disks and relativistic jets. We develop a semi-analytical general relativistic framework that extends classical compressional amplification models by incorporating rotational shear, and apply it to large-scale poloidal magnetic field evolution in accretion flows around a Schwarzschild black hole. By parameterizing the azimuthal velocity as a fraction of the Keplerian value ($ξ\in [0,1]$), from purely radial infall ($ξ=0$) to Keplerian rotation ($ξ=1$), we examine the combined effects of radial compression and shear. Purely radial flows maximize amplification of both $B_r$ and $B_θ$ due to strong compression. In rotating flows, a distinct dichotomy emerges: sub-Keplerian regimes ($ξ<1$) preferentially enhance $B_r$, whereas Keplerian rotation strengthens $B_θ$ via shear. The transition from subsonic outer regions to supersonic relativistic inner regions further accelerates magnetic growth, revealing effects absent in earlier analytical treatments. These results show that rotational support controls both amplification efficiency and magnetic geometry, with sub-Keplerian phases particularly favorable for advecting the radial flux required for MAD formation. This work provides an analytical bridge between classical accretion theory and modern GRMHD simulations, with implications for X-ray binaries, AGNs, and EHT-scale systems.

Coherent perfect tunneling in the presence of loss and asymmetry remains a fundamental challenge in wave transport, a universal problem across optics, acoustics, and quantum mechanics. Here we demonstrate coherent perfect tunneling at an exceptional point in a passive one-dimensional waveguide cascade with three coupled interfaces. Using a waveguide-invariant scattering framework, we show that the suppression of a selected output channel originates from a directional scattering degeneracy rather than from resonance or absorption collapse. This exceptional-point condition emerges when interference between boundary-induced feedback loops promotes a simple zero of the scattering response to a second-order degeneracy. As a direct consequence, fixed coherent excitation produces a robust quartic leakage law within a transparency-dominated tunneling window. These results establish directional degeneracy as a general mechanism for loss-tolerant tunneling enabled by exceptional points across a broad class of wave systems.

Deterministic preparation of high-excitation Fock states is a central challenge in bosonic quantum information, with control complexity that generically explodes as the Hilbert space dimension grows. Here we introduce resonant subspace engineering (RSE), a protocol that analytically confines the infinite-dimensional bosonic dynamics to a two-dimensional invariant subspace spanned by an initial coherent state and the target state. State transfer then reduces to a geodesic rotation on a synthetic Bloch sphere, governed by resonance and phase-matching conditions we derive in closed form. For single Fock states, RSE achieves $O(n^{1/4})$ scaling in both evolution time and gate depth, showing a fundamental improvement over existing deterministic schemes. The construction generalizes to $K$-component superpositions via a $(K{+}1)$-dimensional invariant subspace with full $\mathrm{SU}(K{+}1)$ controllability, requiring only 3-5 iterations of operations for superpositions spanning photon numbers 70--100. RSE provides a scalable and analytically transparent framework for large-scale bosonic state engineering and gate synthesis across single- and multimode platforms.

In Universal Extra Dimension (UED) scenarios, the lightest Kaluza-Klein (KK) particle is naturally stable due to a remnant discrete symmetry, KK parity, arising from extra-dimensional compactification. This stability requires no ad hoc symmetry and renders Kaluza-Klein dark matter a well-motivated candidate, provided it reproduces the observed relic abundance. The minimal UED (mUED) framework being highly predictive is strongly constrained by the combined requirements of relic density and collider searches under standard cosmological assumptions. We revisit the dark matter phenomenology of mUED in the presence of a nonstandard cosmological history featuring a low reheating temperature driven by prolonged inflaton decay. Solving the coupled Boltzmann equations for dark matter, radiation, and inflaton energy densities, we show that entropy injection during reheating can dilute the relic abundance by orders of magnitude, reopening large regions of parameter space previously ruled out. We further demonstrate that the revived parameter space is consistent with current collider, direct-detection, and indirect-detection constraints, while remaining testable by upcoming experiments.

Scalable quantum computers and quantum networks require the combination of quantum processing nodes with efficient light-matter interfaces to distribute quantum information in local or long-distance quantum networks. Neutral-atom arrays have both been coupled to Rydberg states to enable high-fidelity quantum gates in universal processing architectures, and to optical cavities to realize interfaces to photons. However, combining these two capabilities and coupling atom arrays to highly excited Rydberg states in the mode of an optical cavity has been an outstanding challenge. Here we present a novel cavity-coupled Rydberg array that achieves this long-standing goal. We prepare, detect, and control individual atoms in a scalable optical tweezer array, couple them strongly to the optical mode of a high-finesse optical cavity and excite them in a controlled way to Rydberg states. We show that strong coupling to an optical cavity - demonstrated via the dispersive shift of the resonance of the cavity in presence of the atoms - and strong Rydberg interactions - demonstrated via the collective enhancement of Rydberg coupling in the atomic array - can be achieved in our setup at the same spatial location. Our presented experimental platform opens the path to several new directions, including the realization of quantum network nodes, quantum simulation of long-range interacting, open quantum systems and photonic-state engineering leveraging high-fidelity Rydberg control.

The resonating group method (RGM) is widely used to investigate baryon-baryon interactions at the quark level, typically under the assumption that the two baryons involved share an identical harmonic-oscillator frequency. In reality, however, when a specific interaction Hamiltonian is given, different baryons should have unequal oscillator frequencies due to distinct interaction potentials induced by their different quantum numbers. In this work, we develop a new quark-level RGM formalism for baryon-baryon systems with unequal oscillator frequencies, with the aim of describing both single baryons and baryon-baryon interactions in a consistent framework. We present the formalism for solving bound-state and scattering problems, with particular emphasis on constructing the wave functions of two-baryon systems with unequal oscillator frequencies. The proposed formalism is then applied to the $NΔ$ system within a chiral SU(3) quark model, where the quark-quark interaction includes, in addition to the one-gluon exchange (OGE) and a phenomenological confinement potential, the nonet scalar and pseudoscalar meson exchanges arising from the spontaneous breaking of chiral SU(3) symmetry. The distinctive features of the newly developed formalism are elucidated by comparing the results from the new formulation with those from traditional calculations.

Spin networks in Loop Quantum Gravity are traditionally described by unitary holonomies corresponding to noiseless transformations. In this work, we extend this framework to incorporate general quantum channels that model effects of environment, which can become significant at the Planck scale. Specifically, we demonstrate that the transformation properties of Kraus operators, which define completely positive trace-preserving (CPTP) maps, are consistent with the gauge invariance of spin networks. This enables the introduction of generalized spin network states that can be expressed in terms of the Kraus operators. Furthermore, the associated notion of an inner product is proposed, allowing for introduction of the Hilbert space. We illustrate these constructions with examples involving a Wilson loop and a dipole network.

Quantum gas microscopes probe quantum many-body lattice states via projective measurements in the occupation basis, enabling access to various density and spin correlations. Phase information, however, cannot be directly obtained in these setups. Recent experiments went beyond this by measuring local current operators and local phase fluctuations. Here we propose how Fourier-space manipulation in a matter-wave microscope allows access to various long-range off-diagonal correlators in experimentally realistic settings, realizing a many-body phase microscope. We demonstrate in particular how the fermionic d-wave superconducting order parameter in arbitrary Hubbard-type models, the non-equal time Green's function yielding the spectral function, or the hidden order of composite bosons in a fractional Chern insulator can be directly measured. Our results show the great potential of matter-wave microscopy for accessing exotic correlators including phases and coherences and characterizing intriguing quantum many-body states.

The spreading of a thin viscous fluid film on a horizontal surface is an interesting problem in fluid mechanics with many practical applications ranging from coating processes to biological systems and environmental flows. It can even be observed in everyday situations, such as syrup spreading on a pancake. We present a project-based learning approach to this problem, in which engineering or physics undergraduates apply classroom knowledge to understand and solve it, using dimensional analysis, experiments, and theoretical modeling. First, a dimensional analysis is conducted to guide the design of the experiment suitable for an undergraduate laboratory or even at home. The problem is then simplified to obtain a mathematical model that accounts for the experimental results. Through this process, students are able to obtain a solution compatible with those published in fluid mechanics journals with minimal supervision from the instructor. This project not only develops important skills but also motivates students by showing that they have the ability to solve complex problems.

This study presents a tree-level calculation of the scattering amplitude for the $lp\to lpγ$ (with a hard photon) process within the framework of Chiral Perturbation Theory. Our calculations, based on the $O(p^2)$ and $O(p^3)$ nucleon-pion Lagrangians, aim to provide a theoretical prediction for the differential cross-section. The result shows that explicit inclusion of the nonzero lepton mass significantly influences the low energy differential cross section for $μp\to μp γ$ process. The kinematic region of the present experimental data is beyond the validity domain of the $χ$PT and is therefore not suitable for determining the low-energy constants (LECs). By comparing our results with future experimental data, we expect to determine the values of the LECs as a further test of $χ$PT as an effective low-energy theory of QCD. The process is of significant interest as it can help to determine the generalized polarizabilities of the nucleon.

We show that the iterative Faddeev-Jackiw (FJ) reduction for singular Lagrangian systems constitutes a geometrically constrained instance of the Matrix Bordering Technique (MBT). For a first-order Lagrangian with singular pre-symplectic form, each iteration of the Barcelos-Neto-Wotzasek algorithm produces an extended symplectic matrix of canonical bordered form, \begin{eqnarray} f^{(m)} = \left( \begin{matrix} f^{(0)} & B \\ -B^{\mathsf{T}} & 0 \end{matrix} \right) \end{eqnarray} where the bordering block $B$ is determined by the gradients of the consistency constraints. We prove that the nondegeneracy of the extended matrix is governed by the corresponding Schur complement, which is algebraically isomorphic to the Poisson bracket matrix of constraints. As a consequence, the Faddeev-Jackiw algorithm terminates if and only if the constraint algebra is nondegenerate, i.e., when the constraints form a second-class system. This algebraic characterization provides a rigorous foundation for automating the Faddeev-Jackiw procedure symbolically. We present a fully symbolic implementation in the Wolfram Language, and validate the approach on representative mechanical systems with nontrivial constraint structure. The resulting rule-based engine preserves parametric dependencies throughout the reduction, enabling reliable analysis of degeneracy, structural stability (when no bifurcations occur), and possible bifurcation scenarios as critical parameters are varied.

In two-photon polymerization (TPP), the degree of conversion (DC) of the resin has an effect on a broad range of material properties like refractive index (RI) or stiffness. Heterogeneous DC can substitute material doping and multimaterial structures, and outright enable structure designs not possible otherwise. However, obtaining variable DC in the polymer, typically achieved by implementing a variable exposure dose, is held back due to the lack of software support for fabrication and measurement techniques for validation, adding up to a high barrier of entry. This work presents two major breakthroughs in (3+1)D TPP: design freedom and variable-DC fabrication, that are provided by an open-source slicer, as well as calibration methodology for determination of the RI for any DC. Application examples include grayscale lithography, control over writing direction and trajectories, as well as bio-mimicking microphantoms with carefully engineered 3D RI. Results of the RI calibration demonstrate excellent repeatability, accuracy and stability of variable-DC structures. Supported by in-depth metrological analysis, the goal is to popularize variable DC printing within TPP community and to get more out of the existing TPP systems and workflows. In summary, this work provides a complete toolbox for 3D RI engineering and sets the stage for new inventions enabled by point-wise dose control.

The WFC3\IR channel has an innate non-linear response to incident photons, which is corrected for in the calwf3 pipeline with the NLINFILE reference file. The 2009 solution is based on an average polynomial correction for each IR quadrant and is found to be poorly constrained at high fluence levels (e-) approaching the saturation limit. Using a variety of image types, sources, and sample sequences, we test a new pixel-based linearity correction developed by Shenoy et al. (2025). In nearly all cases, the new correction improves the linearity at fluence levels higher than 50,000 e-, with improvements up to 7% for pixels with fluences approaching the saturation limit (80,000 e-) in the last ima reads. The pixel-based solution also significantly decreases the number of cosmic rays erroneously flagged (due to non-linearity correction errors) during ramp fitting in calwf3, leading to improved photometric accuracy in the calibrated flt data and higher signal-to-noise ratios, particularly in Quad 1 (upper-left detector quadrant). Because the new solution tends to make sources brighter, we recalibrate the five HST flux standards used to compute the IR zeropoints and find a negligible impact (0.1-0.2%) on the published values by Calamida et al. (2024), smaller than the RMS dispersion (0.5%) in the observed to synthetic flux ratios for all five flux standards. The new NLINFILE 9au15283i lin.fits was delivered to CRDS in October 2025 and will be used to reprocess all WFC3/IR imaging and grism observations in the MAST archive. An updated reference file a2412448i lin.fits was delivered in February 2026, improving the results at the highest fluence levels by a few tenths of a percent. Please consult the Addendum for details.

Violent cosmic events, from black hole mergers to stellar collapses, often leave behind highly excited black hole remnants that inevitably relax to equilibrium. The prevailing view, developed over decades, holds that this relaxation is rapidly filtered into a linear regime, establishing linear perturbation theory as the bedrock of black hole spectroscopy and a key pillar of gravitational-wave physics. Here we unveil a distinct nonlinear regime that transcends the traditional paradigm: before the familiar linear ringdown, an intrinsically nonlinear, long-lived bottleneck can dominate the evolution. This stage is controlled by a saddle-node ghost in phase space, which traps the remnant and delays the onset of linearity by a timescale obeying a universal power-law. The ghost imprints a distinctive quiescence-burst signature on the emitted radiation: a prolonged silence followed by a violent burst and a delayed ringdown. Rooted in the bifurcation topology, it extends naturally to neutron and boson stars, echoing a topological universality shared with diverse nonlinear systems in nature. Our results expose a missing nonlinear chapter in gravitational dynamics and identify ghost-induced quiescence-burst patterns as clear targets for future observations.